document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119173>Question 1119173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An art history professor assigns letter grades on a test according to the following scheme.\r<BR>\n" );
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document.write( "A: Top 13% of scores\r<BR>\n" );
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document.write( "B: Scores below the top 13% and above the bottom 56%<BR>\n" );
document.write( "C: Scores below the top 44% and above the bottom 21%<BR>\n" );
document.write( "D: Scores below the top 79% and above the bottom 9%<BR>\n" );
document.write( "F: Bottom 9% of scores\r<BR>\n" );
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document.write( "Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734897 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> top 13% is z=+1.128<BR>\n" );
document.write( "z=(x-mean)/sd=(x-79.7)/8.4=1.128<BR>\n" );
document.write( "score=89.18 or 89<BR>\n" );
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document.write( "bottom 56% is 44th percentile and z=-0.15<BR>\n" );
document.write( "score is (x-79.7)=-.15*8.4<BR>\n" );
document.write( "=78.4 or 78<BR>\n" );
document.write( "range is [78, 89]<BR>\n" );
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document.write( "Below top 44 and above the bottom 21<BR>\n" );
document.write( "The top 44 are above z=+0.15 or a score of 80.96 or 81<BR>\n" );
document.write( "Bottom 21% are at z of -0.81 or a score of 72.90 or 73<BR>\n" );
document.write( "so range is [73, 81]\r<BR>\n" );
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document.write( "Top 79% are above the 21st percentile so any score below 73 is below the top 79%.  The bottom 9% are with z=-1.34 so -1.34=(x-79.7)/8.4<BR>\n" );
document.write( "-11.26=x-79.7, so this score is 68.44 or 68<BR>\n" );
document.write( "[68, 73]\r<BR>\n" );
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document.write( "Bottom 9% is <68\r<BR>\n" );
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document.write( " </SPAN>\n" );
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